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a cube = s.o.d . (Posted on 2017-06-15) Difficulty: 3 of 5
I've found a four-digit number ABCD such that
ABCD=(A+B+C+D)3

What is it ?

Is it unique?

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Paper & Pencil solution (spoiler) | Comment 1 of 3
1) the cube root of 9999 is about 21.5, so A + B + C + D <= 21

2) Mod 9, ABCD = A + B + C + D.  Cubing values mod 9, we see that the residues must be 0, 1 or -1.

3) Therefore, A+B+C+D must be in 0,1,8,9,10,17,18, 19

4) Cubing each of these values, we see that two or five work.

    0^3   = 0000
    1^3   = 0001
    8^3   = 0512
    17^3 = 4913
    18^3 = 5832

5) So, no, Ady's value is not unique

Edited on June 16, 2017, 10:18 am
  Posted by Steve Herman on 2017-06-15 09:32:03

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